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Conventional liquids have poor thermal conductivity, thus limiting their use in engineering. Therefore, scientists and researchers have created nanofluids, which consist of nanoparticles dispersed in a base fluid, to improve heat transfer properties in various fields, such as electronics, medicine, and molten metals. In this study, we examine the micropolar nanofluid flow in a stagnation region of a stretching/shrinking sheet by employing the modified Buongiorno nanofluid model. The nanofluid consists of magnetite (Fe3O4) nanoparticles. The similarity equations are solved numerically using MATLAB software. The solution is unique for the shrinking strength λ≥−1. Two solutions are found for the limited range of λ when λc<λ<−1. The solutions terminate at λ=λc in the shrinking region. The rise in micropolar parameter K contributes to the increment in the skin friction coefficient Rex1/2Cf and the couple stress RexMw, but the Nusselt number Rex−1/2Nux and the Sherwood number Rex−1/2Shx decrease. These physical quantities intensify with the rise in the magnetic parameter M. Finally, we investigated the stability of the solutions over time. This work contributes to the dual solution and time stability analysis of the current problem. In addition, critical values of the main physical parameters are also presented. These critical values are usually known as the separation values from laminar to turbulent boundary layer flows. In this case, once the critical value is achieved, the process for the specific product can be planned according to the desired output to optimize the productivity.

This paper provides a strategy for the problem of robust model predictive control of constrained, discrete-time systems with state and output disturbances. Using the linear matrix inequality (LMI) method, the nested geometric proportion asymptotically stable ellipsoid (GPASE) strategy is designed off-line, and then the designed shrinking ellipsoids strategy assures the system converges on the equivalent with an exponential convergence velocity. The biggest advantage of this method is the online computation is almost reduced to zero, which makes it possible to apply the designed control scheme not only to plants with slowly varying parameters, but also to fast ones. Finally, a simulation example shows the validity of the proposed technique.